Robust Cluster Analysis via Mixture Models

Abstract

Finite mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster data sets. In this paper, we focus on the use of normal mixture models to cluster data sets of continuous multivariate data. As normality based methods of estimation are not robust, we review the use of t component distributions. With the t mixture model-based approach, the normal distribution for each component in the mixture model is embedded in a wider class of elliptically symmetric distributions with an additional parameter called the degrees of freedom. The advantage of the t mixture model is that, although the number of outliers needed for breakdown is almost the same as with the normal mixture model, the outliers have to be much larger. We also consider the use of the t distribution for the robust clustering of high-dimensional data via mixtures of factor analyzers. The latter enable a mixture model to be fitted to data which have high dimension relative to the number of data points to be clustered.